dWP function

The Weibull Poisson distribution

Density, distribution function, quantile function, random generation and hazard function for the Weibull Poisson distribution with parameters mu, sigma and nu.

dWP(x, mu, sigma, nu, log = FALSE)

pWP(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)

qWP(p, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)

rWP(n, mu, sigma, nu)

hWP(x, mu, sigma, nu)

Arguments

• x, q: vector of quantiles.
• mu: parameter.
• sigma: parameter.
• nu: parameter.
• log, log.p: logical; if TRUE, probabilities p are given as log(p).
• lower.tail: logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].
• p: vector of probabilities.
• n: number of observations.

Returns

dWP gives the density, pWP gives the distribution function, qWP gives the quantile function, rWP

generates random deviates and hWP gives the hazard function.

Details

The Weibull Poisson distribution with parameters mu, sigma and nu has density given by

$f(x) = \frac{\mu \sigma \nu e^{-\nu}} {1-e^{-\nu}} x^{\mu-1} exp({-\sigma x^{\mu}+\nu exp({-\sigma} x^{\mu}) }),$

for x > 0.

Examples

old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters

## The probability density function
curve(dWP(x, mu=1.5, sigma=0.5, nu=10), from=0.0001, to=2,
      col="red", las=1, ylab="f(x)")

## The cumulative distribution and the Reliability function
par(mfrow=c(1, 2))
curve(pWP(x, mu=1.5, sigma=0.5, nu=10),
      from=0.0001, to=2, col="red", las=1, ylab="F(x)")
curve(pWP(x, mu=1.5, sigma=0.5, nu=10, lower.tail=FALSE),
      from=0.0001, to=2, col="red", las=1, ylab="R(x)")

## The quantile function
p <- seq(from=0, to=0.99999, length.out=100)
plot(x=qWP(p, mu=1.5, sigma=0.5, nu=10), y=p, xlab="Quantile",
     las=1, ylab="Probability")
curve(pWP(x, mu=1.5, sigma=0.5, nu=10),
      from=0, add=TRUE, col="red")

## The random function
hist(rWP(n=10000, mu=1.5, sigma=0.5, nu=10), freq=FALSE,
     xlab="x", ylim=c(0, 2.2), las=1, main="")
curve(dWP(x, mu=1.5, sigma=0.5, nu=10),
      from=0.001, to=4, add=TRUE, col="red")

## The Hazard function
curve(hWP(x, mu=1.5, sigma=0.5, nu=10), from=0.001, to=5,
      col="red", ylab="Hazard function", las=1)

par(old_par) # restore previous graphical parameters

References

Rdpack::insert_ref(key="almalki2014modifications",package="RelDists")

Rdpack::insert_ref(key="Wanbo2012",package="RelDists")

Author(s)

Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co